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Weak Maass-Poincaré series and weight 3/2 mock modular forms. (English) Zbl 1287.11052
J. Number Theory 133, No. 8, 2567-2587 (2013); corrigendum ibid. 159, 434-435 (2016).
Summary: The primary goal of this paper is to construct the basis of the space of weight $$3/2$$ mock modular forms, which is an extension of the Borcherds-Zagier basis of weight $$3/2$$ weakly holomorphic modular forms. The shadows of the members of this basis form the Borcherds-Zagier basis of the space of weight $$1/2$$ weakly holomorphic modular forms. In the course of the construction, we provide a full computation of the Fourier coefficients for the weak Maass-Poincaré series in most general form for the purpose of future reference.

##### MSC:
 11F03 Modular and automorphic functions 11F12 Automorphic forms, one variable 11F30 Fourier coefficients of automorphic forms 11F37 Forms of half-integer weight; nonholomorphic modular forms
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